If a polygon has 26 sides, how many diagonals will it have?

Answer 1

the formula to work out the number of diagonals is:
d=(n/2)(n-3)
where n is the number of sides

therefore the number of diagonal for a 26 sided shape is:
(26/2) x (26-3) = 13 x 23 = 299

Answer 2

It depends what you mean by 'diagonal'. Do you mean lines that join opposite corners? Do you mean lines that join any two corners?

If you mean opposite corners, there would only be 13 diagonals.

If you mean any two corners, then here is my reasoning. Each corner could not make a diagonal with itself or with the corners connected to it by the polygon. For each corner, it will have 23 diagonals. There are 26 corners, each with 23 diagonals. This yields 598. However, you are double counting each diagonal, so you must divide by 2. This yields 299.

Hope this helps.

Answer 3

The way I think about this problem is that you have 26 points so you c(26,2)=325 ways to connect two of them. But 26 of these are sides and not diagonals so 325-26=299.

Answer 4

The formula is:

D=n(n-3)/2

D=26*23/2=299

Your polygon will have 299 diagonals.

Answer 5

For a n-sided polygon, the total is

(1/2)(n(n-1)) - n

So, for n = 26, it's 299

Answer 6

Since it wil also have 26 vertices and each diagonal joins 2 vertices it will have 26/2 = 12 diagonals.

Answer 7

4 sides, 2 diagonals
5 sides, 3 diagonals
...
n sides, n-2 diagonals
26 sides, 24 diagonals

Answer 8

.....pick a vertex-any vertex...it has two neighbours that will not have diagonals connected to it....thus there are 24 diagonals.... an n-gon will have n-2 diagonals with the exception of a triangle....i.e. n>3

Answer 9

299

n(n-3)/2